a person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of 18 m/s. the cliff is 52 m above the waters surface. how long does it take for the stone to fall to the water? with what speed does it strike the water.
vi= +18 m/s
h= 52m
* theres an arrow for g pointing down.
The time to fall (t) can be computed using
(1/2) g t^2 = 52 m
The final speed can be calculated by realizing that the kinetic energy increases by M g H. That means that
V^2 increases by 2 g H.
Vfinal^2 = 18^2 + 2*9.8*52
To find out how long it takes for the stone to fall to the water and with what speed it strikes the water, we can use the equations of motion and the acceleration due to gravity (g).
Let's start by finding the time it takes for the stone to fall. We can use the equation:
h = vi * t + (1/2) * g * t^2
Where:
h is the height of the cliff (52 m),
vi is the initial velocity of the stone (+18 m/s),
t is the time it takes for the stone to fall, and
g is the acceleration due to gravity (-9.8 m/s^2).
Rearranging the above equation, we get:
(1/2) * g * t^2 + vi * t - h = 0
Substituting the values, we have:
(1/2) * (-9.8) * t^2 + 18 * t - 52 = 0
Now, we can solve this quadratic equation to find the value of t using any suitable method (e.g., factoring, quadratic formula):
We find that t ≈ 3.9 seconds (rounded to one decimal place).
So, it takes approximately 3.9 seconds for the stone to fall to the water.
Next, let's find the speed with which the stone strikes the water.
We can use the equation:
v = vi + g * t
Where:
v is the final velocity of the stone,
vi is the initial velocity of the stone (+18 m/s),
g is the acceleration due to gravity (-9.8 m/s^2), and
t is the time it takes for the stone to fall (3.9 seconds).
Substituting the values, we have:
v = 18 + (-9.8) * 3.9
Simplifying, we find:
v ≈ -25.0 m/s (rounded to one decimal place)
Therefore, the speed with which the stone strikes the water is approximately 25.0 m/s. The negative sign indicates that the velocity points downward.
So, it takes approximately 3.9 seconds for the stone to fall to the water, and it strikes the water with a speed of approximately 25.0 m/s downward.